Related papers: Universal Log-Optimality for General Classes of e-…
Hypothesis testing via e-variables can be framed as a sequential betting game, where a player each round picks an e-variable. A good player's strategy results in an effective statistical test that rejects the null hypothesis as soon as…
Algorithms for hyperparameter optimization abound, all of which work well under different and often unverifiable assumptions. Motivated by the general challenge of sequentially choosing which algorithm to use, we study the more specific…
We study the problem of stochastic contextual bandits in the agnostic setting, where the goal is to compete with the best policy in a given class without assuming realizability or imposing model restrictions on losses or rewards. In this…
The problem of sequential probability forecasting is considered in the most general setting: a model set C is given, and it is required to predict as well as possible if any of the measures (environments) in C is chosen to generate the…
We consider the classical question of predicting binary sequences and study the {\em optimal} algorithms for obtaining the best possible regret and payoff functions for this problem. The question turns out to be also equivalent to the…
We propose a framework which generalizes "decision making with structured observations" by allowing robust (i.e. multivalued) models. In this framework, each model associates each decision with a convex set of probability distributions over…
In this paper, we consider the problem of simultaneous testing of multivariate normal means under arbitrary covariance dependence. Specifically, let $\boldsymbol{X}\sim N_n(\boldsymbol{\theta},\boldsymbol{\Sigma})$, where…
We address the problem of learning to control an unknown nonlinear dynamical system through sequential interactions. Motivated by high-stakes applications in which mistakes can be catastrophic, such as robotics and healthcare, we study…
Probabilistic classifiers are central for making informed decisions under uncertainty. Based on the maximum expected utility principle, optimal decision rules can be derived using the posterior class probabilities and misclassification…
In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the…
We study the problem of expert advice under partial bandit feedback setting and create a sequential minimax optimal algorithm. Our algorithm works with a more general partial monitoring setting, where, in contrast to the classical bandit…
The expected improvement (EI) algorithm is one of the most popular strategies for optimization under uncertainty due to its simplicity and efficiency. Despite its popularity, the theoretical aspects of this algorithm have not been properly…
We suggest a new approach to hypothesis testing for ergodic and stationary processes. In contrast to standard methods, the suggested approach gives a possibility to make tests, based on any lossless data compression method even if the…
We address the problem of sequential prediction with expert advice in a non-stationary environment with long-term memory guarantees in the sense of Bousquet and Warmuth [4]. We give a linear-time algorithm that improves on the best known…
We analyze the problem of sequential probability assignment for binary outcomes with side information and logarithmic loss, where regret---or, redundancy---is measured with respect to a (possibly infinite) class of experts. We provide upper…
We study sequential prediction of real-valued, arbitrary and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from…
The composite binary hypothesis testing problem within the Neyman-Pearson framework is considered. The goal is to maximize the expectation of a nonlinear function of the detection probability, integrated with respect to a given probability…
Off-policy learning and evaluation leverage logged bandit feedback datasets, which contain context, action, propensity score, and feedback for each data point. These scenarios face significant challenges due to high variance and poor…
In this paper we study the adaptivity of submodular maximization. Adaptivity quantifies the number of sequential rounds that an algorithm makes when function evaluations can be executed in parallel. Adaptivity is a fundamental concept that…
In this paper, we study gap-dependent regret guarantees for risk-sensitive reinforcement learning based on the entropic risk measure. We propose a novel definition of sub-optimality gaps, which we call cascaded gaps, and we discuss their…